Question

In any triangle ABC if a=18,b=24 ,c=30 find cosA ,cosB,cosC

Answer 1

Okay so in order to have Cos A and Cos B we first need to have a right triange.

Prove of Triangle ABC is right angles triangle:
LHS= RHS=
AC^2 BC^2+AB^2=(24×24)+(18+18)=576+324=900
=900
LHS=RHs
Hence AND is right angled triangle

I think so you meant AB=18, BC=24 and CA=30 or else it would mean angle.

Now, Case I

Cos A= Adjacent/ Hypotenuse

So,
Adjacent=AB= 18
Hypotenuse=AC= 30

Cos A=18/30= 9/15

Case II

Cos B=Adjecent/ Hypotenuse
Adjacent= BC= 24
Hypotenuse= CA= 30

So,

Cos B= BC/CA= 24/30= 4/5

Hope so you got the answer.

Answer 2

Answer:

Step-by-step explanation:

a = 18, b = 24, c = 30 gives C = 90 degrees as a^2 + b^2 = c^2 then

cos A = b/c = 24/30 = 4/5 ANSWER

verify trigonometrically

cos A = (b^2 + c^2 -- a^2) / 2bc = (24^2 + 30^2 -- 18^2) / 2*24*30 = 1152/1440 = 4/5

cos B = a/c = 18/30 = 3/5 ANSWER

cos C = cos (90) = 0 ANSWER

sin A = a/c = 18/30 = 3/5 ANSWER

sin B = b/c = 24/30 = 4/5 ANSWER

sin C = sin (90) = 1 ANSWER